Texture characterization is an important technique in medical image analysis. Image texture is defined as the spatial relationship of pixel values in an image region. In medical images, texture is associated with a local characteristic pattern of image intensity that identifies a tissue. Texture also determines local spectral or frequency content in an image. Changes in local texture causes changes in the local spatial frequency. Texture characterization is of interest in medical imaging because as biological tissues become abnormal during a disease process, their underlying textures also change.
Various techniques for characterizing image textures—including statistical; Fourier, and wavelet based techniques—have been applied to radiological images indicative of numerous pathologies such as, for example, multiple sclerosis, brain tumors, liver diseases, and malignant breast lesions, as well as normal tissues.
A texture feature is a value that quantifies a characteristic of local intensity variation within an image. A common technique for quantifying image texture used in medical imaging is based on co-occurrence matrices. Statistical measures of texture are calculated based on the frequency of specific grey levels occurring between pairs of points within an image. The co-occurrence technique has been used, for example, to classify benign and malignant solitary pulmonary nodules in Computed Tomography (CT) images and to quantify pathological changes during treatment of multiple sclerosis. However, the co-occurrence technique is limited to very small Regions Of Interest (ROIs) due to its computational complexity. Therefore, only textures associated with the highest frequencies are revealed. Broad, large-scale changes are difficult to detect using co-occurrence techniques. Furthermore, the resulting statistical measures are difficult to interpret and compare from one patient to another.
A more advanced method of texture analysis is based on discrete wavelet analysis. Wavelets provide a multi-scale representation of an image, allowing analysis of varying degrees of detail within an image. Wavelet-based texture analysis has been used for automated diagnosis and grading of breast tumor histology images.
The Stockwell-Transform (ST) is closely related to the continuous wavelet transform using a complex Morlet mother wavelet and using the ST local spatial frequency content of each pixel in an image is directly determined. The ST has been used in numerous applications such as, for example, geophysics, hydrology, and power systems analysis. The one-dimensional ST has been a useful tool for analysis of signals in medical applications such as, for example, EEG, functional magnetic resonance imaging and laser Doppler flowmetry. The ST is well suited for texture analysis of medical images due to its space-frequency resolution and for its close connection to the Fourier transform—the basis of medical image reconstruction. The ST uses complex Fourier basis functions modulated by frequency-dependent Gaussian windows. The ST preserves the phase information, uses a linear frequency scale and is easily inverted for recovering an image in the Fourier domain.
The computational complexity of the ST technique has been a main obstacle in applications of ST-based texture analysis for 2D images. Extensive processing time and large memory are used for calculating and storing the texture descriptions of 2D medical images. The 2D ST of an array of size N×N has a computational complexity of O[N4+N4 log(N)] and uses a storage space of O[N4]. As a result, the ST of a typical 256×256 pixel MR image takes approximately 1.5 hours to calculate on a single computer and uses 32 GB of memory. Therefore, the ST-based texture analysis of 2D images has been limited to small ROIs and collapsed to one-dimensional spectra. However, small ROIs reduce the resolution of the frequency spectra and, therefore, the sensitivity to subtle texture changes, rendering the application of the 2D-ST in a clinical environment difficult and impractical. Clinical texture analysis requires a fast, efficient process that provides information about substantially all frequency components.
Despite these limitations, application of the 2D-ST has shown promising results in identifying differences in texture that correlate with neurological pathology, for example, in detecting sub-clinical abnormalities in Normal Appearing White Matter (NAWM) of multiple sclerosis patients, or in identifying brain tumors.
It is desirable to provide a method for texture characterization of image data using a 2D ST that is efficient with regard to data processing and data storage.
It is also desirable to provide a method for texture characterization of image data using rotationally invariant features of the 2D ST.